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ALBERTO CAVALLOMassachusetts Institute of Technology

GUILLERMO CRUCESUniversidad Nacional de La Plata

RICARDO PEREZ-TRUGLIAMicrosoft Research

Learning from Potentially Biased Statistics

ABSTRACT When forming expectations, households may be influenced by perceived bias in the information they receive. In this paper, we study how individuals learn from potentially biased statistics using data from both a natural experiment and a survey experiment during a period (2007–15) when the government of Argentina was manipulating official inflation statistics. This period is interesting because attention was being given to inflation informa-tion and both official and unofficial statistics were available. Our evidence suggests that, rather than ignoring biased statistics or naively accepting them, households react in a sophisticated way, as predicted by a Bayesian learning model. We also find evidence of an asymmetric reaction to inflation signals, with expectations changing more when the inflation rate rises than when it falls. These results could also be useful for understanding the formation of inflation expectations in less extreme contexts than Argentina, such as the United States and Europe, where experts may agree that statistics are unbiased but households are not.

Household inflation expectations play a key role in models of consump-tion decisions and the real effects of monetary policy, yet little is known

about how these expectations are formed. In recent years, a growing body of empirical literature has been providing evidence about how individuals use information to form their inflation expectations. For example, in Cavallo, Cruces, and Perez-Truglia (2014), we show that individuals learn from both inflation statistics and supermarket prices. In this paper, we use data from a period of manipulated official statistics in Argentina to study the degree of sophistication in this learning process and the role of trust in statistics.

60 Brookings Papers on Economic Activity, Spring 2016

Our findings are based on observational and experimental evidence obtained in Argentina during the recent period, from 2007 to 2015, when the government manipulated inflation statistics. This is an ideal setting, for three main reasons. First, the inflation rate fluctuated between 15 and 30 percent, which led to high inattention costs and encouraged individu-als to spend time gathering and processing information about the inflation rate.1 Second, ample evidence suggests that the official sources of inflation information, such as the Consumer Price Index (CPI), were intentionally biased.2 And third, the lack of reliable official data during this period pro-moted the creation of several unofficial inflation indicators, thereby poten-tially allowing individuals to counteract the government’s manipulation by using other data.

We start with observational data on the comovement of inflation expec-tations and official and unofficial inflation statistics, both before and after the intervention by the Argentine government’s statistics bureau, Instituto Nacional de Estadística y Censos (INDEC), when the government started reporting official statistics that were systematically below the unofficial estimates. Household inflation expectations quickly diverged from the offi-cial inflation indicators and instead aligned with the unofficial indicators. This change suggests that consumers are not naive learners who accept official statistics as unbiased. However, this observational evidence pres-ents two challenges. First, we do not observe the distribution of expecta-tions in the counterfactual scenario without manipulated official statistics. Second, the evidence does not address the nature of the learning process, such as whether individuals simply ignore official statistics or use their information in a sophisticated way.

To address these limitations in the observational data, we provide a sim-ple model of Bayesian learners with potentially biased statistics and design a survey experiment to test its predictions. This model shows that, far from ignoring official statistics, rational learners should react to changes in offi-cial statistics by “debiasing” the signal on the basis of their perceived bias

1. Because they cannot write contracts in foreign currency or indexed by inflation, households needed to constantly estimate inflation to sign rent contracts, negotiate wages, and make savings and investment decisions. Indeed, during the period we are studying, infla-tion statistics were frequently mentioned and discussed in the front pages of newspapers and other media outlets, and opinion polls systematically indicated that inflation was perceived as one of the most important problems in the country.

2. For a discussion of the evidence for the manipulation of statistics, see Cavallo (2013). Our paper extends the account of the main events from 2006 until December 2015, when a new government finally suspended the publication of the official CPI.

ALBERTO CAVALLO, GUILLERMO CRUCES, and RICARDO PEREZ-TRUGLIA 61

while simultaneously updating their beliefs about the size of the official bias. In other words, we predict that rational consumers will extract useful information from potentially biased information.

In December 2012, we conducted a survey experiment in Argentina to test this prediction. We provided respondents with different inflation estimates, and we measured their subsequent inflation perceptions and inflation expectations, as well as their confidence in these perceptions. By leveraging the variety of inflation indicators available at the time, we cross-randomized, in a nondeceptive way, two features of the message that was provided to subjects: the source of the inflation statistics (official and unofficial), and the inflation rate (10, 20, or 30 percent).

Our experimental evidence rejects the hypothesis that individuals ignore information from biased official statistics. Subjects reacted significantly to all signals, including official statistics. For example, compared with individ-uals who were told that the official inflation rate was 20 percent, individuals who were told that it was 10 percent reported lower inflation perceptions and expectations, and individuals who were told that it was 30 percent reported higher ones.

The experimental data also allow us to directly test the hypothesis that there may be sophisticated learning from potentially biased statistics. Because the official statistics were consistently 10 percentage points below the unofficial estimates, our Bayesian model predicts that individuals should react similarly to a signal that official inflation is 10 percent as they would to a signal that unofficial inflation is 20 percent, and that they should react similarly to an official rate of 20 percent as they would to an unofficial rate of 30 percent. These predictions are consistent with subjects’ reactions in our experiment. That is, in an environment where there are many alter-native inflation indicators and much attention is being given to the topic, individuals function as sophisticated learners who can deal with potentially biased information.

The experiment also allowed us to explore another pattern found in our analysis of the observational data: Expectations follow actual inflation more strongly when actual inflation is rising than when it is falling. Consistent with this asymmetric pattern, we find that subjects were nearly twice as reactive to new information about higher inflation as they were to informa-tion about lower inflation, even when the information came from unofficial sources. Indeed, we discuss the possibility that this asymmetric learning was generated by the introduction of manipulated statistics.

A group of studies suggests that individuals form inflation expecta-tions using information from their own consumer experiences (Bates and


Gabor 1986; Bruine de Bruin, van der Klaauw, and Topa 2011; Coibion and Gorodnichenko 2015; Kumar and others 2015; Malmendier and Nagel 2016). In particular, individuals rely heavily on their perceptions about the prices of individual supermarket products (Cavallo, Cruces, and Perez-Truglia 2014). These findings imply that the government could try to influ-ence inflation expectations by changing the actual prices of salient products. Indeed, in an effort to curb inflation, in 2013 the Argentine government froze the prices of a relatively large and important sample of consumer prod-ucts. We show that, even though the inflation rate then fell significantly, household inflation expectations did not fall. To further explore this find-ing, we ran a price-elicitation survey outside a large supermarket chain in Argentina during the period of price controls. We found that even though there was a substantial difference in the actual price changes between goods that were under price controls and those that were not, consumers did not perceive such price differences.

Although the context of manipulated statistics in Argentina is an extreme case, these results can nonetheless help to explain how individuals learn from inflation data in other countries. Even in developed nations, a sig-nificant share of individuals do not trust official statistics. For instance, according to a Eurobarometer report by the European Commission (2010), 71 percent of respondents in Europe in 2009 felt that it was necessary to know about economic indicators, but only 44 percent stated that they tended to trust official statistics such as the growth rate, the inflation rate, and the unemployment rate.3 Among U.S. survey respondents, 27 percent rated their trust in official statistics as 4 or lower on a scale of 1 to 10 (Curtin 2009). Analysts, commentators, and the media routinely discuss the pos-sibility of manipulated statistics, such as those that may have been reflected in the job creation rates that were released right before the 2012 election in the United States (Norris 2014).

Data from a survey of U.S. households reported in Cavallo, Cruces, and Perez-Truglia (2014) show that 32 percent of respondents do not trust official inflation statistics. Furthermore, compared with those who trust inflation statistics, respondents who do not trust statistics have inflation expectations that are 50 percent higher on average. This evidence sug-gests that a lack of trust in the government may explain part of the stylized

3. In the 2007 wave of the survey, 69 percent of respondents felt it was necessary to know about economic indicators, and 46 percent stated they tended to trust official statistics. See European Commission (2010, pp. 35, 44).


fact that households do not fully incorporate information from inflation statistics into their perceptions and expectations (Mankiw and Reis 2002; Mankiw, Reis, and Wolfers 2004; Carroll 2003).

To the best of our knowledge, this paper is the first to study how individuals learn from manipulated statistics. More generally, the study of biased statis-tics goes back to the seminal contribution by Oskar Morgenstern (1963) on measurement, accuracy, and uncertainty in economics. Morgenstern’s book discusses how both private companies and governments have strong incen-tives to manipulate information, and he applies this argument to the prob-lems of measuring prices.4 Recent studies use data to measure the degree of bias in official statistics, including examples of inflation in Argentina (Cavallo 2013), debt manipulation indicators in Greece (Rauch and others 2011), and alternative growth and inflation estimates in China (Nakamura, Steinsson, and Liu 2014). Tomasz Michalski and Gilles Stoltz (2013), in turn, use statistical regularities in economic indicators to suggest that countries seem to manipulate economic data systematically.

Our paper also relates to a growing body of literature on the formation of household economic expectations. In particular, it is widely recognized that identifying the formation of inflation expectations is important to understand the link between the nominal and real sides of the economy (Bernanke 2007; Coibion and Gorodnichenko 2015; Bachmann, Berg, and Sims 2015; D’Acunto, Hoang, and Weber 2016). Several studies pro-vide evidence that inflation statistics play a significant role in driving inflation expectations, including the analysis of variation in the media’s coverage of statistics (Lamla and Lein 2008; Badarinza and Buchmann 2009; Dräger 2015), quasi-experimental variation in reporting official sta-tistics (Carrillo and Emran 2012), and information-provision experiments (Roos and Schmidt 2012; Armantier and others 2016; Cavallo, Cruces, and Perez-Truglia 2014).

Finally, this paper relates to a theoretical literature about whether central banks (or other government agencies) should commit to pro-vide timely and accurate information about economic fundamentals. For instance, some authors argue that information disclosure enhances welfare (Hellwig 2005), whereas others argue that it can reduce welfare

4. Morgenstern (1963) also covers the difficulties of measuring the national product, and in fact Argentina’s government also falsified INDEC’s GDP indicator (Camacho, Dal Bianco, and Martinez-Martin 2015), for political reasons and to avoid the payment of a GDP warrant (a bond that only pays debtors if the GDP grows at a certain rate).


(Morris and Shin 2002). The majority of these studies focus on the margin of disclosing truthful information or not. We focus on a margin that has been widely overlooked: manipulating the information that is disclosed.

The paper proceeds as follows. Section I describes the period of manip-ulation of official statistics in Argentina and presents the observational evidence. Section II presents a simple model of Bayesian learning from manipulated statistics, as well as the design of the survey experiment and its results. In section III, we discuss the period of price controls in 2013. Section IV concludes.

I. The Manipulation of Inflation Statistics in Argentina

This section describes the main events related to the manipulation of offi-cial inflation statistics, as well as the emergence of unofficial estimates and their comovement with consumers’ inflation expectations.

I.A. The Government’s Intervention at INDEC

After a severe economic crisis in 2001–02, the Argentine economy started to recover in 2003, mostly due to an unprecedented increase in com-modity prices. Inflation levels were relatively low at the beginning of the recovery, but they reached double digits in 2005 (12.3 percent per year).

Figure 1 provides a timeline of the most important events from 2006 to 2015. During 2006, the government imposed a series of price controls and organized public boycotts against some retailers. The government also pres-sured the professional staff at INDEC to make methodological changes that could lower the annual inflation rate. For example, the government asked INDEC to reveal which stores were collecting data, to introduce automatic substitutions to reduce the weight from items that had higher inflation, and to use prices from goods on price control lists even if those goods were not available for sale at the stores where the data were being collected.

In February 2007, facing a second year of inflation above 10 percent and unwilling to scale back its expansionary monetary policy, the govern-ment made the drastic decision to fire high-ranking members of the INDEC staff, including Graciela Bevacqua, the statistician in charge of the team that computed the CPI. The monthly inflation rate fell from 1.1 percent in January 2007 to 0.4 percent in February and continued falling in the sub-sequent months. INDEC’s employees publicly disclosed what had hap-pened in the previous months, which increased suspicions that the CPI was being manipulated. INDEC stopped publishing several disaggregated


Figure 1. Timeline of the Manipulation of Inflation Statistics in Argentina, 2006–16

Sources: Various newspaper articles and other sources, compiled by the authors.

Feb 2006 ● The secretary of interior commerce, Guillermo Moreno, tries to gain access to micro data protected by statistical confidentiality laws

Oct 2006 ● Moreno hires a market-research firm, Tomadato, to produce an alternative CPI Jan 2007 ● The director of INDEC announces that Beatriz Paglieri, Moreno’s assistant, will be

visiting the institution for one month to check the last estimations ● First meeting with Paglieri and the directors of INDEC ● Paglieri decides to stop the publication of the CPI for the greater Buenos Aires

metropolitan area, the CPI-GBA ● Graciela Bevacqua, the director of the Prices Department, is suspended Feb 2007 ● The government officially intervenes at INDEC ● The first manipulated CPI-GBA monthly index is published ● Bevacqua is officially fired and replaced by Paglieri ● First mobilization of INDEC employees takes place (repeated every month since) ● Senators from the opposition ask a federal prosecutor to intervene Mar 2007 ● The director of INDEC, Leilo Marmora, resigns May 2007 ● Manuel Garrido, a federal prosecutor, says serious irregularities took place at INDEC Jul 2007 ● Cynthia Pok, in charge of the National Household Survey, is fired ● First official strike by INDEC employees Sep 2007 ● INDEC modifies Mendoza province’s inflation rate before publication ● The calculation of the CPI-Nacional is changed Dec 2007 ● Cristina Kirchner becomes the president of Argentina, succeeding her husband Jan 2008 ● INDEC employees receive wage cuts Mar 2008 ● Launch of www.inflacionverdadera.com, a website where alternative indicators using

online prices are updated on a daily basis; the inflation rate is three times higher than official CPI estimates

May 2008 ● INDEC stops publishing the CPI-Nacional, an index that used price data from seven provinces

● INDEC announces new CPI weights; food becomes more important in the new index ● Some employees of INDEC are physically assaulted by government supporters at the

Finance Ministry building Nov 2010 ● The government announces an agreement with the International Monetary Fund for

the normalization of the statistics Feb 2011 ● Moreno asks private consultants to share the methodology of their CPI calculations;

most of them refuse Mar 2011 ● Some private consultants are fined 500,000 pesos for failing to comply with

Moreno’s request May 2011 ● The Congress Average index (an average of private consultants’ inflation rates) is born ● A judge rejects the fines imposed on private consultants Sep 2011 ● Private consultants receive letters from the government threatening them with

criminal prosecution if they continue to publish their own inflation estimates Feb 2012 ● The International Monetary Fund announces that Argentina did not improve the

CPI-GBA according to the international rules ● The Economist stops publishing Argentina’s official statistics and uses instead the index

produced by PriceStats (a company working with the Billion Prices Project at MIT) Feb 2013 ● The International Monetary Fund issues a “motion of censure” against Argentina for

the bad-quality statistics ● Moreno is replaced by Augusto Costa as Secretary of Interior Commerce Jan 2014 ● The CPI-GBA is replaced by a new index, called CPI-Nu; it initially shows similar

monthly inflation rates to unofficial estimates, but starts to diverge once again within a few months

Apr 2014 ● The government announces that the official poverty index will no longer be published Dec 2015 ● Mauricio Macri, a member of the opposition, becomes the new president of Argentina ● Jorge Todesca becomes INDEC’s director, and Bevacqua returns as its technical

director ● Todesca says that INDEC is like a “scorched earth,” and suspends publication of the

CPI and other price indexes Jan 2016 ● Bevacqua announces that it will take eight months for INDEC to publish a new CPI Feb 2016 ● Bevacqua is fired again


inflation series, and it announced “methodological changes” that were never publicly disclosed.

The government’s intervention at INDEC had immediate negative con-sequences for the Argentine economy, as discussed by Eduardo Levy Yeyati and Marcos Novarro (2013). Although the government paid less in the short run on inflation-linked bonds, most of this debt was held by the govern-ment’s own pension funds. The price of these bonds quickly fell, as inves-tors internalized the manipulation. The government also paid much higher interest rates for newly issued debt.5 Economic uncertainty increased, bank deposits fell, and capital outflows surged, which eventually, in 2011, led the government to impose foreign exchange controls. Despite the contro-versy and the negative effects on the economy, the manipulation of the official CPI continued until December 2015, when a new government was elected.

I.B. Unofficial Inflation Statistics

INDEC’s unusual situation led to the creation of alternative measures of inflation, which we generally term “unofficial” inflation indicators. The main alternative indicator we use is computed by PriceStats, a private firm based in the United States that since 2007 has been using online prices from large retailers. The PriceStats index is published weekly in The Economist.6 A second alternative indicator, published since 2008, is produced by the orga-nization named Buenos Aires City, a think tank led by Graciela Bevacqua (the former head of INDEC’s CPI team that was fired by the government in 2007). Buenos Aires City uses prices collected from a sample of products in the city of Buenos Aires and follows the old INDEC methodology.7

A third unofficial indicator is the Provincial Index, based on CPIs from nine Argentine provinces. Whereas the official national index by INDEC was historically based only on the greater Buenos Aires area, provincial statistical agencies also collected regional price data and computed their own CPIs. The federal government pressured the provinces to manipulate or stop publishing these indexes, but those provinces that were not aligned

5. For example, in 2008 the government paid an interest rate of 15 percent for newly issued debt sold to the government of Venezuela.

6. PriceStats is a private company connected with the Billion Prices Project, an academic initiative based at the Massachusetts Institute of Technology (MIT) that was created in 2008 by Alberto Cavallo and Roberto Rigobon to experiment with the use of online data in the pro-duction of price indexes and other macroeconomic and international research applications. For details of the Billion Prices Project, see Cavallo and Rigobon (2016).

7. For the details, see Bevacqua and Salvatore (2009).


with the federal government continued disseminating their own unadulter-ated data. This index is computed as a geometric, weighted mean of nine provincial CPIs for the post-2006 period, with weights computed to maxi-mize the correlation between the provincial aggregate and the official index (based on greater Buenos Aires) during the pre-manipulation period. Finally, the Congress Average index is an average of private inflation indicators that were widely cited in the media in 2011, after the government started to fine and prosecute economists who were publishing their own unofficial infla-tion estimates. Some members of Congress from the opposition political parties, who were immune from prosecution, compiled and published a monthly average of “private” estimates. Other alternative indicators also were publicized. The online appendix provides a comprehensive list, with characteristic details and methodologies.8

Figure 2 shows the annual inflation rate for all these unofficial indica-tors and the official CPI. The vertical line shows the month of the inter-vention at INDEC, where the official and unofficial indicators immediately diverged. All unofficial indicators showed similar results, despite differ-ences in their data sources and methodologies. On average, the inflation rate in the unofficial indicators was approximately 10 percentage points higher than that in the official data.

I.C. Inflation Expectations and Inflation Statistics

The surge in inflation during 2006 motivated a renewed interest in the measurement of household expectations. In August 2006, the Finance Research Center (Centro de Investigación en Finanzas) at Torcuato Di Tella Uni versity began a national household survey of inflation expectations.

In figure 3, we plot the official inflation rate, our main unofficial infla-tion indicator (PriceStats), and the median inflation expectation from the household survey. These monthly time series allow us to study the coevolu-tion of available inflation indicators and of inflation expectations for seven years of uninterrupted manipulation of official statistics.

Over time, household inflation expectations aligned with the unofficial inflation level. The PriceStats index was not disseminated until March 2008, but newspapers reported other unofficial estimates before then.9 In the online

8. The online appendixes for this and all other papers in this volume may be found at the Brookings Papers web page, www.brookings.edu/bpea, under “Past Editions.”

9. An earlier version of the PriceStats index started to be published in a website called www.inflacionverdadera.com in March 2008.


appendix, we plot the annual inflation rates mentioned in these newspaper articles and show that they track inflation expectations during 2007.

There is also some evidence of an asymmetric response of inflation expec-tations to the actual inflation rate. Two periods in particular show sticky expectations on the way down. First, from September 2008 to July 2009, when the country was experiencing the effects of the global financial crisis, the unofficial inflation rate fell by 13 percentage points, but median infla-tion expectations fell by only 7 percentage points. Second, from December 2012 to July 2013, due to both significant price controls and another reces-sion, the unofficial inflation rate fell by 5 percentage points, but inflation

Sources: INDEC; PriceStats LLC; Cavallo and Rigobon (2016); Cosas que Pasan (CqP); Bevacqua and Salvatore (2009).

a. The vertical line represents the start of the government’s intervention at INDEC in January 2007. All inflation indicators are monthly series.

b. Annual inflation rate based on a geometric, weighted mean of nine provincial statistical agencies’ CPIs. c. Annual inflation rate based on an average of several unofficial indicators compiled by Congress represen-

tatives from opposition parties.d. Annual inflation rate compiled by the organization named Buenos Aires City from a sample of products

and prices from the greater Buenos Aires metropolitan area, following INDEC’s traditional methodology (the two series coincide until September 2006). According to Bevacqua and Salvatore (2009), this index uses data from the Mendoza provincial index in 2007 and from a “private consulting firm” (possibly PriceStats) in 2007. This could explain the similarities seen with the other indexes at those times.

e. Annual inflation rate compiled by PriceStats LLC based on prices from online retailers. f. Annual inflation rate reported by INDEC based on a sample of prices from the greater Buenos Aires

metropolitan area.

30

25

20

10

15

5

Percent

2005 2007 2009 2011 2013Year

Officialf

PriceStatse

Provincial Indexb

Buenos Aires Cityd

Congress Averagec

Figure 2. Official Inflation and Alternative Unofficial Indicators, 2004–13a


expectations increased by 1 percentage point. We discuss this asymmetric reaction in the next section, including the possibility that statistical manipu-lation caused this asymmetry. The observational evidence suggests that, if anything, manipulating inflation statistics made things worse from the point of view of curbing inflation expectations.

II. Experimental Evidence

The patterns that emerge from the time series analyzed in the previous section support the hypothesis that individuals are not naive learners who accept official statistics without question. However, we cannot make causal inferences from these observational data, and it is unclear whether indi-viduals are simply ignoring the official data or are adjusting to them in a

Figure 3. Official Statistics, Unofficial Statistics, and Inflation Expectations, 2006–13a

Sources: INDEC; PriceStats LLC; Cavallo and Rigobon (2016); Torcuato Di Tella University, Finance Research Center (Centro de Investigación en Finanzas), Inflation Expectations Survey (Encuesta de Expectativas de Inflación).

a. The vertical line represents the start of the government’s intervention at INDEC in January 2007. b. Quarterly averages of the monthly median of inflation expectations for the following 12 months from

the Encuesta de Expectativas de Inflación. This survey collects information on the inflation expectations for the following 12 months among the general population of Argentina, based on a standard question such as, “What do you expect the annual rate of inflation will be during the next 12 months?”

c. Annual inflation rate compiled by PriceStats LLC based on prices from online retailers. d. Annual inflation rate reported by INDEC based on a sample of prices from the greater Buenos Aires

metropolitan area (monthly series).

30

20

10

Percent

Year2007 2009 2011 2013

Officiald

Unofficialc

Expectationsb


rational way. To address these limitations, this section develops a Bayesian learning model of inflation expectations in the presence of biased signals, and it uses experimental evidence to test some of its predictions.

II.A. A Model of Learning with Biased Statistics

For the sake of simplicity, we study the static case where the inflation rate is fixed at pactual and an individual must learn about this rate of inflation indirectly from a series of signals. We also assume that price changes for each individual product in the economy are normally distributed with mean pactual and variance s2

actual, and that the variance is known to the individual. Relaxing these assumptions would complicate the algebra but would not change the model’s main intuition.

The individual can observe two signals based on the information about the price changes for individual products. The first signal comes from the price changes for a randomly drawn subset of Nu products, with an asso-

ciated mean u− and variance σ12

Nu

actual. This signal could be an unbiased,

unofficial inflation index or could represent the information that individu-als obtain by using averages of their own memories about price changes for a set of products. The second signal is the government’s official statistics. We assume that the government also takes a randomly drawn subset of No products and computes its average price change, producing a signal with

associated mean o− and variance σ12

No

actual. However, the government does

not report o− but instead adds a bias, bactual, before reporting it. In other words, the government reports o−′ = o− + bactual instead of o−. Note that Nu and No determine the precision of the unofficial and official signals. To simplify

notation, we replace s2u = σ1

2

Nu

actual and s2o = σ1

2

No

actual.10

The individual has two beliefs: one about the inflation rate, p, and another about the government bias, b. We denote p0 as the belief about the inflation rate before obtaining new information, and p1 as the belief about the inflation rate after doing so; and b0 and b1 are similarly defined. The normality assumption about the distribution of price changes determines

10. In practice, s2u and s2

o represent not only pure statistical errors driven by sample size but also other sources of error. For example, individuals may perceive s2

o to be high because they do not understand how precise these statistics are or because they do not believe that these statistics are representative of their own consumption bundle. Similarly, s2

u may take into account the individual’s imprecision in remembering historical prices.


that the conjugate distribution for beliefs about inflation and bias is bivariate normal. For the sake of notational simplicity, we focus on the case where the prior beliefs about the inflation rate and the bias are orthogonal. As shown in the online appendix, this assumption leads to these posterior beliefs:

u o b1 11 1 2 0 1 2 0( ) ( )( ) π = − ω − ω π + ω + ω ′−

b b o o u2 1 .1 1 2 0 1 0 2( ) ( ) ( )( ) = − ψ − ψ + ψ ′− π + ψ ′−

The mean posterior belief about the inflation rate, p1, is a weighted aver-age between the mean prior belief, p0; the unofficial inflation rate, u−; and the bias-adjusted official statistics, o−′ - b0. The mean posterior belief about government bias, b1, is a weighted average between the prior belief, b0; the gap between the official statistics and the prior belief about inflation, o−′ - p0; and the gap between the official statistics and the unofficial statis-tics, o−′ - u−. The parameters w1, w2, y1, and y2 are weights that depend on the precision of the signals and prior beliefs. Details about these weights are provided in the online appendix.

The most important prediction of this model is that a Bayesian learner is not expected to ignore biased statistics, but instead rationally adjust to the perceived bias. The following two scenarios are useful for understanding this model’s intuition.

The first scenario explores how an individual who starts thinking that the government is not lying reacts to an official signal that is different from its prior. In particular, consider an individual who starts with b0 = 0 and gets signals u− = p0 (the unofficial signal equals the prior) and o−′ < p0 (the official signal is lower than the prior). The individual can attribute the low level of the official statistic to a bias, or can believe that it is driven by sampling vari-ation. How fast would the individual learn about a bias? By making the rel-evant replacements in the formula given above for b1, we get b1 = (y1 + y2) (o−′ - p0). The term y1 + y2 is a set of weights that increases with the preci-sion of both the official and unofficial signals. So, for example, if the indi-vidual perceived that there is a lot of measurement error in either of those signals, he or she would not so rapidly change his or her belief about a bias in the official data.

The second scenario explores how an individual who believes that the government is manipulating statistics reacts to the official statistics com-pared with the unofficial statistics. In the next sections, we study this sce-nario by means of a series of information experiments during the period of manipulated statistics. Consider an individual who starts out thinking


that the government biases the inflation statistics downward; that is, b0 < 0. How does the individual react to official statistics compared with unofficial statistics? From the formula for p1, it follows that, qualitatively, the indi-vidual reacts to o−′ in the same way as he or she reacts to u−, but with the exception that first it subtracts from o−′ the ex ante perceived bias; that is, it uses o−′ - b0 instead of o−′. So if the individual believes that the bias is b0 = -10 percent, then he or she should react qualitatively to the signal o−′ = 10 percent in the same way that he or she reacts to u− = 20 percent. These reactions are qualitatively the same but potentially quantitatively very dif-ferent, because the weights w1 and w2 could be potentially very different. For instance, these weights would be very different if there is a large differ-

ence in precision between the unofficial and official statistics, σ1

2u

and σ1

2o

.

However, if these statistics are similarly precise, then we would expect a reaction that is quantitatively very similar.11

II.B. The Experimental Design

The survey experiment in this section is related to a group of recent studies on how individuals learn about inflation and how they form their infla-tion expectations (Roos and Schmidt 2012; Armantier and others 2016; Cavallo, Cruces, and Perez-Truglia 2014). We first collect background information about respondents (see the online appendix for a translation of the questionnaire). We then randomly assign subjects to different groups. The control group receives no information. The other informational treat-ments receive either official or unofficial statistics about inflation rates for the previous 12 months. After the information provision, we elicit sub-jects’ inflation perceptions and expectations and measure how a particular signal about inflation affects the distribution of inflation perceptions and expectations.

The inflation perceptions correspond to a question about current infla-tion levels (that is, the respondent’s perception of the annual inflation rate during the previous 12 months). We also include a question about the respondents’ subjective assessments of their confidence in their answers, measured on a scale from 1 (“not at all confident”) to 4 (“very confident”).

11. Note that even if the precision of unofficial and official statistics were exactly the

same, σ

=σ

1 1,

2 2u o

we would still have w1 > w2, and thus the individual would react more to u−

than to o b .0′ − The reason is that, when doing the correction o−′ - b0, the individual is using b0, which has some uncertainty of its own.


The subject’s inflation expectations correspond to the expected inflation rate during the following 12 months. Argentina’s economic history implies that the general public understands the meaning of the word “inflation,” which is discussed routinely in the media.12 Thus, when eliciting inflation perceptions and expectations, we state our question using the word “infla-tion,” instead of referring to “changes of prices in general” or other indirect references to inflation that are commonly used in U.S. surveys and in other low-inflation countries.13

The message about inflation provided in the survey experiment has the following structure:

According to [SOURCE], the annual inflation rate with respect to a year ago was approximately [X percent].

In this message, [SOURCE] could be “one of the official indicators pub-lished by INDEC” (that is, official statistics) or “one of the unofficial indi-cators published by consulting firms, analysts, and research centers” (that is, unofficial statistics). The large variety of inflation indicators allows us to cross-randomize two features of this message in a nondeceptive way: the source of the inflation statistics (official or unofficial), and the inflation rate (10, 20, or 30 percent).

For the official statistics, the first indicator produced by INDEC is the CPI, which is the most common inflation index in the world. This was the main indicator targeted for government manipulation. At the time of our experiment, the annual growth rate of the official CPI was approximately 10 percent. INDEC also computed other indicators that reflected differ-ent inflation levels. One was the GDP deflator, which is sometimes used as a measure of inflation and which closely tracked the CPI in Argentina before 2007. At the time of the experiment, the GDP deflator was close to

12. Moreover, the previous rounds of the online opinion poll, into which we built our survey experiment, used the wording in terms of inflation, as did other sources for infla-tion expectations, such as the Inflation Expectations Survey (Encuesta de Expectativas de Inflación) conducted by the Finance Research Center (Centro de Investigación en Finanzas) at Torcuato Di Tella University. Also, we did not provide any incentives for respondents to answer accurately, such as prizes for guessing the right figures. As shown by Armantier and others (2011) in the context of similar studies, there is a significant correlation between incen tivized and nonincentivized responses on inflation expectations.

13. For instance, the University of Michigan’s Survey of Consumers elicits inflation expectations by means of the following questions: “During the next 12 months, do you think that prices in general will go up, or go down, or stay where they are now?”—with three options, “go up,” “stay the same,” and “go down”—and then asks, “By about what percent do you expect prices to change, on average, during the next 12 months?” with an open numerical answer.


20 percent. The government could not allow the GDP deflator to be as low as the CPI (10 percent), because that would have implied an implausibly high real GDP growth rate (more than 15 percent). We also use a third statistic compiled by INDEC and routinely used by local economists as an inflation proxy: the rate of growth of nominal wages. At the time of our survey, this measure indicated an annual inflation rate close to 30 percent. We followed a similar strategy to exploit the variation in unofficial statistics. We chose one index published by an unofficial source that indicated an inflation rate close to 20 percent, and another index that indicated an inflation rate close to 30 percent. A third unofficial index, published by a think tank with close ties to the government, indicated an inflation rate close to 10 percent.

We emphasize that we did not deceive the experimental subjects; we conveyed information from the public discussion in Argentina at that time. We did not claim that the information provided was true or false; nor did we endorse or disavow, implicitly or explicitly, any of the sources. We merely stated that, according to a given source, the level of annual inflation was estimated to be X percent. In any case, because individual judgment about the information can vary depending on the source, we included a debriefing statement at the end of the survey. In this statement, we disclosed that the information about inflation that we provided was randomly selected from six possible messages, and we included a detailed source and explanation for each message. We presented the same statement to all subjects, irre-spective of their assigned treatment group. Our purpose was that the sub-jects should leave the experiment with more information than what they had at the beginning of the experiment.

II.C. The Subject Pool and Experimental Results

The sample and survey are based on the ones used by an established pub-lic opinion research firm that carries out a quarterly online survey of adults in Argentina, which has had a stable set of questions since 2011. The exper-iments were conducted in December 2012, while the government was still manipulating official statistics, and almost six years after the government started to do this manipulation. We slightly modified the standard format of this public opinion survey to fit our experimental design. In particular, our survey experiment was included early in the questionnaire’s flow, after which it continued with the usual set of questions about politics, politicians, and public affairs. These questions are not used to determine outcomes in our analysis, although we use some of them for descriptive purposes and to verify the balance between treatment groups. The respondents were assigned to the control group with a probability of 22.6 percent, and to each of the


treatment groups with a probability of 12.9 percent. The final sample on which the following analysis is based consists of all the respondents who completed the questions on inflation perceptions and inflation expectations, yielding a final sample of 3,138 observations.14

Table 1 presents summary statistics about the demographics of the sample, along with the corresponding indicators for the general population. This sample is not representative of the general Argentine population; though it is roughly similar in age and gender composition, our sample is substan-tially more educated and richer than average. Nevertheless, the qualitative results are similar if we reweight the observations to match the distribution of characteristics at the national level (not reported).

Table 2 presents descriptive statistics for all the variables used in the analysis, including pretreatment and posttreatment variables, for the con-trol group and for each of the treatment groups. The last column reports

14. A small but nonnegligible number of individuals abandoned the questionnaire after the information treatment and the question on inflation perceptions, and before reporting their inflation expectations (105 out of 3,243, or 3.24 percent of the original sample). Although this type of attrition also occurred in previous rounds of the opinion poll (for instance, the sample had a dropout rate of 5.8 percent for the June 2012 round), in this case this might be a concern if the attrition were due to (and correlated with) the information treatments, because this could introduce biases in the experiment and complicate the interpretation of the treat-ment effects. For instance, government supporters who believe that inflation is low may have abandoned the experiment because they did not like to see information from unofficial sources reporting high inflation levels (the opposite situation could arise with respondents opposed to the government and with high inflation perceptions). However, this does not seem to be a concern in practice, because we cannot reject the null hypothesis of equal attrition across treatment groups (p value = 0.79).

Table 1. Descriptive Statistics for the Online Opinion Survey Sample and Argentina’s Total Populationa

Share female Mean age

Share living in greater

Buenos Aires

Share with college degreeb

Share who voted for Kirchnerc

Authors’ sample 0.570 41.1 0.677 0.607 0.242Argentina’s

population 0.528 44.9 0.363 0.156 0.541

Sources: Authors’ online opinion survey (see text); INDEC, Annual Survey of Urban Households (Encuesta Anual de Hogares Urbanos); the 2011 presidential election results.

a. All statistics are based on individuals ages 20 or older. The sample size for the authors’ online opinion survey is 3,138.

b. Share of respondents who have completed college or another form of postsecondary education.c. Share of respondents who reported voting for Cristina Kirchner in the 2011 presidential election.

Tabl

e 2.

Ave

rage

Pos

ttre

atm

ent a

nd P

retr

eatm

ent R

espo

nses

, by

Trea

tmen

t Gro

upa

Con

trol

Offi

cial

– 10

per

cent

Offi

cial

– 20

per

cent

Offi

cial

– 30

per

cent

Uno

ffici

al–

10 p

erce

ntU

noffi

cial

– 20

per

cent

Uno

ffici

al–

30 p

erce

ntp

valu

eb

Post

trea

tmen

tIn

flat

ion

perc

epti

on,

prev

ious

12

mon

ths

28.3

1(0

.591

)28

.55

(0.8

12)

33.5

8(0

.809

)42

.10

(0.8

15)

26.3

7(0

.805

)28

.89

(0.8

09)

34.7

8(0

.816

)<

0.0

1

Con

fide

nce

in in

flat

ion

perc

epti

onc

-0.0

903

(0.0

319)

0.11

9(0

.043

8)-0

.014

4(0

.043

7)-0

.119

(0.0

440)

0.01

22(0

.043

5)0.

0804

(0.0

437)

0.09

12(0

.044

1)<

0.0

1

Infl

atio

n ex

pect

atio

n,

follo

win

g 12

mon

ths

28.2

0(0

.595

)28

.22

(0.8

17)

33.3

2(0

.814

)39

.24

(0.8

20)

26.2

9(0

.810

)28

.62

(0.8

14)

33.9

9(0

.821

)<

0.0

1

Pre

trea

tmen

tS

hare

fem

ale

0.56

0(0

.018

1)0.

539

(0.0

248)

0.56

3(0

.024

7)0.

586

(0.0

249)

0.60

1(0

.024

6)0.

545

(0.0

247)

0.60

8(0

.025

0)0.

28

Age

41.1

1(0

.390

)41

.06

(0.5

36)

40.6

4(0

.534

)40

.79

(0.5

38)

40.9

3(0

.532

)41

.37

(0.5

34)

41.1

6(0

.539

)0.

97

Sha

re w

ith

coll

ege

degr

eed

0.63

3(0

.017

8)0.

610

(0.0

245)

0.65

0(0

.024

4)0.

581

(0.0

246)

0.57

2(0

.024

3)0.

600

(0.0

244)

0.57

8(0

.024

6)0.

12

Ow

n ec

onom

ic

situ

atio

n is

bet

tere

0.26

1(0

.015

5)0.

237

(0.0

213)

0.22

8(0

.021

2)0.

203

(0.0

214)

0.23

3(0

.021

1)0.

257

(0.0

212)

0.21

1(0

.021

4)0.

26

No.

of

obse

rvat

ions

750

397

400

394

404

400

393

Sour

ce: A

utho

rs’ o

nlin

e op

inio

n su

rvey

(se

e te

xt).

a. E

ach

cell

repr

esen

ts t

he m

ean

of e

ach

of t

he r

ow v

aria

bles

for

the

cor

resp

ondi

ng c

ontr

ol a

nd t

reat

men

t gr

oups

in

the

colu

mn

head

ers.

Tre

atm

ent

grou

ps a

re b

roke

n do

wn

by re

spon

dent

s’ s

ourc

e of

infla

tion

stat

istic

s (o

ffici

al o

r uno

ffici

al),

and

the

sour

ce’s

repo

rted

infla

tion

rate

(10,

20,

or 3

0 pe

rcen

t). S

tand

ard

erro

rs a

re in

par

enth

eses

.b.

Rep

orts

the

p va

lue

of a

bal

ance

test

in w

hich

the

null

hypo

thes

is is

that

the

mea

n of

eac

h va

riab

le is

equ

al b

etw

een

all s

even

exp

erim

enta

l gro

ups

(the

con

trol

gro

up

and

the

six

trea

tmen

t gro

ups)

.c.

Rep

rese

nts

the

resp

onde

nt’s

ow

n co

nfide

nce

in h

is o

r he

r re

spon

se to

the

perc

eptio

ns q

uest

ion

on a

sca

le o

f 1

(“no

t con

fiden

t at a

ll”)

to 4

(“v

ery

confi

dent

”).

d. S

hare

of

resp

onde

nts

who

hav

e co

mpl

eted

col

lege

or

anot

her

form

of

post

seco

ndar

y ed

ucat

ion.

e. S

hare

of

resp

onde

nts

who

rep

orte

d th

at th

eir

curr

ent e

cono

mic

situ

atio

n w

as b

ette

r co

mpa

red

with

12

mon

ths

earl

ier.


the p value of a test in which the null hypothesis is that the mean of each variable is equal in all seven experimental groups. As expected, these tests are not rejected for any of the pretreatment variables, suggesting that the randomization was indeed balanced. The top panel shows the posttreatment variables: inflation perceptions, confidence in these perceptions, and infla-tion expectations. We discuss this impact in more detail below. Addition-ally, the main experimental results are presented in two complementary ways. In figure 4 just below, we show the distribution of inflation percep-tions in the control group compared with that of each of the six other infor-mational treatments. And figure 6 below summarizes the effects of the six informational treatments on the means of various posttreatment outcomes relative to the control group.

Our benchmark results in this section are based on the effects on infla-tion perceptions, which are directly related to the information signals pro-vided by the experiment (past 12 months’ data), but they are equivalent to those that are obtained from inflation expectations, as we discuss below.

We begin by measuring whether individuals’ inflation perceptions were influenced by the messages with unofficial statistics. The left-side panels of figure 4 show the distribution of perceptions in the control group and each of the messages about the unofficial statistics. The data suggest that individ-uals did not ignore this information; compared with individuals who were told that inflation according to official statistics was 20 percent, individuals who were told that official statistics were lower (10 percent) reported lower inflation perceptions, and individuals who were told that official statistics indicated higher inflation (30 percent) reported higher perceptions. We con-ducted the Epps–Singleton (ES) two-sample test using the empirical char-acteristic function, a version of the Kolmogorov–Smirnov test of equality of distributions valid for discrete data (Goerg and Kaiser 2009). According to the ES test, all these pairwise differences are statistically significant at the 1 percent level. Additionally, these differences are economically significant. In sum, individuals seemed eager to learn from unofficial sources.

The first hypothesis to test is whether individuals reacted at all to the messages about official statistics. The right-side panels of figure 4 show the distribution of perceptions in the control group and each of the messages about the official statistics. In comparison with individuals who were told that inflation according to official statistics was 20 percent, individuals who were told that official statistics were lower (10 percent) reported lower inflation perceptions, and individuals who were told that official statistics indicated higher inflation (30 percent) reported higher inflation percep-tions. According to the ES test, these pairwise differences in distributions

2030 10Perc

ent

Infl

atio

n pe

rcep

tions

(pe

rcen

t), p

revi

ous

12 m

onth

s

Uno

ffic

ial–

10 p

erce

ntb

Bel

ow 56

to 1011

to 1516

to 2021

to 2526

to 3031

to 3536

to 4041

to 4546

to 5051

to 55A

bove

56

Bel

ow 56

to 1011

to 1516

to 2021

to 2526

to 3031

to 3536

to 4041

to 4546

to 5051

to 55A

bove

56

2030 10Perc

ent

Infl

atio

n pe

rcep

tions

(pe

rcen

t), p

revi

ous

12 m

onth

s

Uno

ffic

ial–

20 p

erce

ntd

2030 10Perc

ent

Infl

atio

n pe

rcep

tions

(pe

rcen

t), p

revi

ous

12 m

onth

s

Off

icia

l–10

per

cent

c

Bel

ow 56

to 1011

to 1516

to 2021

to 2526

to 3031

to 3536

to 4041

to 4546

to 5051

to 55A

bove

56

Bel

ow 56

to 1011

to 1516

to 2021

to 2526

to 3031

to 3536

to 4041

to 4546

to 5051

to 55A

bove

56

2030 10Perc

ent

Infl

atio

n pe

rcep

tions

(pe

rcen

t), p

revi

ous

12 m

onth

s

Off

icia

l–20

per

cent

e

Con

trol

Tre

atm

ent

Figu

re 4

. H

isto

gram

s Co

mpa

ring

the

Dis

trib

utio

n of

Infla

tion

Perc

eptio

ns b

etw

een

Trea

tmen

t and

Con

trol

Gro

upsa

Sour

ce: A

utho

rs’ o

nlin

e op

inio

n su

rvey

(se

e te

xt).

a.

Pan

el c

aptio

ns in

dica

te th

e tr

eatm

ent g

roup

. Res

pond

ents

in th

e tr

eatm

ent g

roup

wer

e gi

ven

nond

ecep

tive

info

rmat

ion

abou

t inf

latio

n es

timat

es f

rom

uno

ffic

ial (

left

-sid

e pa

nels

) or

off

icia

l (ri

ght-

side

pan

els)

sou

rces

. Res

pond

ents

in th

e co

ntro

l gro

up w

ere

not g

iven

any

info

rmat

ion

abou

t inf

latio

n st

atis

tics.

The

re w

ere

750

obse

rvat

ions

in th

e co

ntro

l gro

up.

The

his

togr

ams

are

cens

ored

at

5 pe

rcen

t an

d 56

per

cent

(in

clus

ive)

, bu

t th

ese

bins

rep

rese

nt t

he c

umul

ativ

e ob

serv

atio

ns b

elow

5 p

erce

nt a

nd a

bove

56

perc

ent,

resp

ectiv

ely.

The

E

pps–

Sing

leto

n p

valu

e is

a m

easu

re o

f th

e eq

ualit

y of

the

two

dist

ribu

tions

(G

oerg

and

Kai

ser

2009

).b.

Res

pond

ents

wer

e to

ld th

at th

e an

nual

infl

atio

n ra

te w

ith

resp

ect t

o a

year

ago

was

app

roxi

mat

ely

10 p

erce

nt a

ccor

ding

to a

n un

offi

cial

sou

rce.

The

re w

ere

404

obse

rvat

ions

in

the

trea

tmen

t gro

up. E

pps–

Sin

glet

on p

val

ue <

0.0

1.

c. R

espo

nden

ts w

ere

told

that

the

annu

al in

flat

ion

rate

wit

h re

spec

t to

a ye

ar a

go w

as a

ppro

xim

atel

y 10

per

cent

acc

ordi

ng to

an

offi

cial

sou

rce.

The

re w

ere

397

obse

rvat

ions

in

the

trea

tmen

t gro

up. E

pps–

Sin

glet

on p

val

ue <

0.0

1.

d. R

espo

nden

ts w

ere

told

that

the

annu

al in

flat

ion

rate

wit

h re

spec

t to

a ye

ar a

go w

as a

ppro

xim

atel

y 20

per

cent

acc

ordi

ng to

an

unof

fici

al s

ourc

e. T

here

wer

e 40

0 ob

serv

atio

ns in

th

e tr

eatm

ent g

roup

. Epp

s–S

ingl

eton

p v

alue

= 0

.06.

e.

Res

pond

ents

wer

e to

ld th

at th

e an

nual

infl

atio

n ra

te w

ith

resp

ect t

o a

year

ago

was

app

roxi

mat

ely

20 p

erce

nt a

ccor

ding

to a

n of

fici

al s

ourc

e. T

here

wer

e 40

0 ob

serv

atio

ns in

th

e tr

eatm

ent g

roup

. Epp

s–S

ingl

eton

p v

alue

< 0

.01.

f.

Res

pond

ents

wer

e to

ld th

at th

e an

nual

infl

atio

n ra

te w

ith

resp

ect t

o a

year

ago

was

app

roxi

mat

ely

30 p

erce

nt a

ccor

ding

to a

n un

offi

cial

sou

rce.

The

re w

ere

393

obse

rvat

ions

in

the

trea

tmen

t gro

up. E

pps–

Sin

glet

on p

val

ue <

0.0

1.

g. R

espo

nden

ts w

ere

told

that

the

annu

al in

flat

ion

rate

wit

h re

spec

t to

a ye

ar a

go w

as a

ppro

xim

atel

y 30

per

cent

acc

ordi

ng to

an

off

icia

l sou

rce.

The

re w

ere

394

obse

rvat

ions

in

the

trea

tmen

t gro

up. E

pps–

Sin

glet

on p

val

ue <

0.0

1.

Bel

ow 56

to 1011

to 1516

to 2021

to 2526

to 3031

to 3536

to 4041

to 4546

to 5051

to 55A

bove

56

2030 10

2030 10

Perc

ent

Infl

atio

n pe

rcep

tions

(pe

rcen

t), p

revi

ous

12 m

onth

s

Uno

ffic

ial–

30 p

erce

ntf

Bel

ow 56

to 1011

to 1516

to 2021

to 2526

to 3031

to 3536

to 4041

to 4546

to 5051

to 55A

bove

56

Perc

ent

Infl

atio

n pe

rcep

tions

(pe

rcen

t), p

revi

ous

12 m

onth

s

Off

icia

l–30

per

cent

g


are statistically significant at the 1 percent level. These differences are economically significant; for instance, the mean of inflation perceptions is 28.5 percent for the official–10 percent group, 33.6 percent for the official– 20 percent group, and 42.1 percent for the official–30 percent group.

The second hypothesis to test is the naive learning hypothesis, accord-ing to which households react to information on a given level of infla-tion from an official source in the same way that they would react to the same figure if it were coming from unofficial sources. The data strongly reject this hypothesis; the ES test indicates that the difference between the distribution of inflation perceptions across individuals given messages official–10 percent and unofficial–10 percent is significant at the 1 percent level; the same is true when comparing the distribution of perceptions for the official–20 percent and unofficial–20 percent groups, and for the official–30 percent and unofficial–30 percent groups. These differences are not only statistically but also economically significant—for instance, compared with the unofficial–10 percent, the message official–10 percent created inflation perceptions that were 2.1 percentage points higher; com-pared with the unofficial–20 percent, the message official–20 percent created inflation perceptions that were 4.7 percentage points higher; and compared with the unofficial–30 percent, the message official–30 per-cent created inflation perceptions that were 7.3 percentage points higher.

The third hypothesis to test is the rational learning hypothesis. A plau-sible heuristic for the period under study is that official inflation rates were systematically 10 percentage points below those from unofficial sources. On the basis of this approximation, the learning model predicts that indi-viduals should react to information conveying an official inflation level of X percent in the same way as they would react to information from unofficial sources conveying a level of inflation of X - 10 percent. The results from our experiment are consistent with this hypothesis; we cannot reject the null hypothesis that the distributions of inflation perceptions are equal between individuals in the groups official–10 percent and unofficial– 20 percent (ES p value = 0.91), and we cannot reject the null hypothesis that the distributions of inflation perceptions are equal between individu-als with the messages official–20 percent and unofficial–30 percent (ES p value = 0.61). These differences are not only statistically insignifi-cant; they are also economically small. For instance, the difference in the mean perceived inflation is only 0.34 percentage point between the official–10 percent and unofficial–20 percent groups, and 1.2 percentage points between the official–20 percent and unofficial–30 percent groups.


The experiment also allows us to further explore the seemingly asym-metric relationship between perceived and actual inflation suggested by the analysis of the nonexperimental time series data discussed in the pre-vious sections. According to table 2, increasing the unofficial inflation rate shown to the subject from 10 percent to 20 percent also increased the mean perceived inflation rate by 2.52 percentage points (p value < 0.05). Instead, increasing the unofficial inflation rate shown to the subject from 20 percent to 30 percent, which is also an increase of 10 percentage points, raised the mean perceived inflation rate by 5.89 percentage points (p value < 0.01). That is, the effect of going from 20 percent to 30 percent is almost twice the size of the effect of going from 10 percent to 20 percent, and this difference is statistically significant (p value = 0.072). This evidence suggests that individuals were twice as reactive to information about higher inflation than to information about lower inflation. The results are similar for those who received signals from official sources; inflation per-ceptions are 5 percentage points lower in the official–10 percent group than in the official–20 percent group, and they are 8.5 percentage points lower in the official–20 percent compared with the official–30 percent group. The difference between these two effects is statistically significant (p value = 0.082).

This asymmetry in the experimental effects is consistent with the observa-tional evidence analyzed in section I.C. In a related paper (Cavallo, Cruces, and Perez-Truglia 2014) we find no evidence of asymmetry in the reaction to information about the price changes of supermarket products, which sug-gests that the asymmetry is particular to inflation statistics. Furthermore, it is possible that this asymmetry was generated by the manipulation of offi-cial statistics, although we do not have experimental evidence preceding the period of manipulation to test this hypothesis directly. According to this conjecture, when individuals observe an inflation statistic indicating that inflation is below their prior belief, they suspect that such a statistic may be subject to government bias, even if it comes from a nongovernmental agency, and thus they put less weight on learning from this piece of informa-tion. On the contrary, because the government’s goal is to reduce inflation perceptions, individuals do not worry that a statistic has a government-induced bias when it suggests that inflation is above their prior belief, thus explaining the asymmetry.15

15. Note that this conjecture predicts that the asymmetry would be reversed if the government were interested in increasing rather than reducing inflation perceptions.


Perceptions about past inflation are a key input in the formation of infla-tion expectations (Jonung 1981; Cavallo, Cruces, and Perez-Truglia 2014). For instance, figure 5 shows a binned scatter plot of the relationship between inflation perceptions and inflation expectations in our experimental sample, based on the subsample of respondents in the control group. This figure shows that, as expected, these two variables are strongly associated. If our information treatments affected inflation perceptions, we would expect to observe a similar effect on inflation expectations. The comparison of effects between the top and middle panels of figure 6 indicates that the effects on perceived inflation (top panel) were very similar to the effects on infla-tion expectations (middle panel). For instance, compared with the control group, the unofficial–30 percent message increased inflation perceptions by 6.47 percentage points and inflation expectations by 5.79 percentage points, with the difference between the two effects being close to zero and statistically insignificant.

Additionally, the bottom panel of figure 6 shows the effect of the dif-ferent treatments on the subjects’ reported confidence in their inflation

Source: Authors’ online opinion survey (see text).a. There are 777 observations in the control group. Respondents in the control group were not given any

information about inflation statistics.

80

60

40

20

Inflation expectations (percent), next 12 months

Inflation perceptions (percent), previous 12 months20 40 60 80

ScatterBinned scatter

Linear fit, slope = 0.834

Figure 5. Past Inflation Perceptions and Future Inflation Expectations for the Control Groupa


Figure 6. Treatment Effects on Inflation Perceptions and Expectationsa

Source: Authors’ online opinion survey (see text). a. Each bar represents the point estimate of the effect of the specific subtreatment compared with the control

group. Respondents in the control group were not given any information about inflation statistics. See notes to figure 4 for sample sizes. Robust standard errors are reported.

b. Mean effect on the treatment groups’ inflation perceptions for the previous 12 months compared to the control group. The mean perceived inflation rate for the control group is 28.31 percent.

c. Mean effect on the treatment groups’ inflation expectations for the following 12 months compared with the control group. The mean expected inflation rate for the control group is 28.2 percent.

d. Mean effect on the treatment groups’ confidence in perceived inflation compared with the control group, which received no information about inflation statistics. A respondent’s confidence is reported on a scale from 1 (“not confident at all”) to 4 (“very confident”).

Effect on inflation perceptions (percent)0 5 10 15

15

Perceived inflationb

Official–10 percent



Unofficial–10 percent















Effect on inflation expectations (percent)0–5

–5

5 10

Expected inflationc

Effect on confidence in inflation perceptions0–0.1 0.1 0.2 0.3

Confidence in perceived inflationd


perceptions, coded from 1 (“not confident at all”) to 4 (“very confident”). Bayesian learning predicts that, after observing a useful signal, individuals should usually be more confident about their posterior beliefs relative to the counterfactual with no information. The bottom panel of figure 6 indi-cates that, as expected, several of the informational treatments significantly increased the subjects’ reported confidence in their inflation perceptions. Interestingly, the effect on reported confidence is almost twice as large for unofficial statistics (1.15) than for official statistics (0.86; p value of the difference = 0.066), suggesting that the information from unofficial sources was on average more useful.

Note that part of the reaction to the information provided in the experiment may be spurious, for example, due to numerical anchoring or experimenter-demand effect. This is an important concern because, as shown in Cavallo, Cruces, and Perez-Truglia (2014), only about half the reaction to the infla-tion information provided in similar survey experiments is genuine rather than spurious. In any case, according to the results from our earlier paper, it is plausible that the effects identified in this paper are quantitatively dif-ferent, but qualitatively robust to spurious learning.

III. The 2013 Price Controls

Studies suggest that individuals form inflation expectations using informa-tion from their own consumer experiences, such as their memories of the prices of supermarket products (Bates and Gabor 1986; Bruine de Bruin, van der Klaauw, and Topa 2011; Cavallo, Cruces, and Perez-Truglia 2014; Coibion and Gorodnichenko 2015; Kumar and others 2015). This implies that the government could try to manipulate inflation expectations by changing the actual prices of salient products. This section discusses evi-dence about a 2013 effort by the government to control the prices of super-market products.

In February 2013, the government of Argentina significantly extended its policy of price controls on retail products. These “price agreements” with big companies and large supermarket chains were temporarily applied to hundreds of products in carefully selected categories. The government targeted goods that had a significant weight in the CPI basket, and it focused on brands and retailers with large market shares. To enforce these price controls, the government publicly asked its supporters to help moni-tor prices. The program, which was called Precios Cuidados (Protected Prices), was widely advertised and discussed in the media. Although there were some problems with its implementation, most of the goods included


in the agreements were available for sale at the agreed-on prices. It is pos-sible that the government hoped that by controlling the prices of key indi-vidual goods, it could influence inflation expectations. Consistent with this interpretation, the finance minister repeatedly mentioned that the price controls were meant to “provide predictability to the economy.”16

The inflation rate did temporarily fall; according to the unofficial sta-tistic of PriceStats shown in figure 3 above, the annual inflation rate fell from 25.8 percent in January 2013 to 17.7 percent in May 2013. This is not surprising, given that the PriceStats index draws its data mostly from large multichannel retailers (which sell both online and offline), where the gov-ernment was focusing its price control efforts. Even though the inflation rate did fall, figure 3 suggests that there was no effect on inflation expecta-tions, which remained stable, at near 30 percent.

There are several possible explanations for this lack of an effect on infla-tion expectations. One possibility is that people knew the effect would be temporary, so expectations about future inflation were not affected. This probably played an important role, but we do not have a way to test it. Another possibility is that even though people experienced more stable prices for some goods, this information did not affect their perceptions of prices. To test this, we ran a consumer-intercept survey at the front doors of four branches of one of the largest supermarket chains in the city of Buenos Aires, during the period of the price controls. The subject pool consisted of supermarket customers who, having just made a purchase, were invited to participate in a short survey for an academic study. Using hand-held scanners, our inter-viewers scanned respondents’ receipts from their supermarket purchases, which contained product identifiers that were matched to a database of scraped online data from the same supermarket.17 After their receipts were scanned, respondents were asked about the current prices of the products they had just purchased, and the corresponding prices as of 12 months before.

The top panel of figure 7 depicts the distribution of actual price changes for products with controlled prices, and for those with no controls. The figure shows that products with controlled prices did have a substantially lower inflation rate—with an average change of 1.9 percent, compared with 21.7 percent for noncontrolled products. However, the bottom panel of figure 7 shows that the program was not effective in changing individual

16. For example, see https://www.scribd.com/doc/312284129/Precios-Cuidados.17. Prices were scraped from the websites of the supermarket by the Billion Prices

Project at MIT. See Cavallo (2013) for details.


Figure 7. Actual and Remembered Price Changes for Products with Government-Controlled Pricesa

Source: Authors’ consumer-intercept survey (see text). a. Respondents were asked about price changes with respect to 12 months earlier for products they had just

purchased at the supermarket. The total number of observations is 1,140.

20

15

10

5

Percent

Price change (percent), previous 12 months

−20 orless

−19 to–10

−9 to0

1 to10

11 to20

21 to30

31 to40

41 to50

51 to60

61 to70

71 to80

81 to90

90 ormore

−20 orless

−19 to–10

−9 to0

1 to10

11 to20

21 to30

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61 to70

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30

20

10

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Price change (percent), previous 12 months

Actual price changes

Remembered price changes

Government-controlled pricesNot government-controlled prices

Government-controlled pricesNot government-controlled prices


perceptions of price changes; the distribution of remembered price changes (as reported by the consumers) are very similar, and statistically indistin-guishable, between controlled and noncontrolled products.18 In any case, just as happens with the manipulation of the aggregate official index, price controls did not seem to be an effective way to influence inflation expecta-tions, at least not in the short term.

IV. Conclusions

To understand how households learn from potentially biased statistics, we utilize data from a natural experiment and a survey experiment based on the period when the Argentine government manipulated inflation statistics. We find that consumers are sophisticated users of information. Rather than simply ignoring biased statistics or accepting them as unbiased, individuals can effectively adjust for the perceived bias using other available infor-mation. Furthermore, the publication of biased statistics may have led to an asymmetric reaction to inflation signals, even the unbiased ones, with expectations changing more when inflation rises than when it falls. The gov-ernment’s attempt to manipulate inflation expectations seems to have been ineffective and plausibly counterproductive.

These lessons are useful for understanding the formation of inflation expectations in less extreme contexts than Argentina, such as in the United States and Europe, where experts may believe that statistics are unbiased but the general population does not. For example, using data on a survey of U.S. households reported in Cavallo, Cruces, and Perez-Truglia (2014), we find that 32 percent of respondents did not trust the official inflation data and had inflation expectations that were significantly higher than the rest. The average inflation expectation for the group that did not trust the official statistics was 6.36 (standard error = 7.19), compared with an average of 4.22 (standard error = 4.26) in the rest of the sample (p value of the difference < 0.01). Our study suggests that the difference could be driven by the way individuals adjust for perceived biases in the official data. One policy implication is that governments should focus on provid-ing information and make efforts to reduce the perception of a potential

18. It is important to note that individuals were roughly accurate in remembering the current prices of the products that they just purchased, and that—even among the non-controlled goods—the remembered price changes had a large and systematic upward bias (results not reported).


bias. This lesson may be relevant for inflation statistics as well as other governmental statistics.

For policymakers, our results are useful for better understanding the pro-cess of belief formation in contexts of increasing inflation. In particular, as the Federal Reserve and other counties’ central banks return to a more neu-tral monetary policy, these results, together with our other research, imply that the process whereby inflation expectations are formed may quickly change. As inflation rises, individuals devote more attention to inflation and adjust their expectations accordingly. Inflation expectations that may seem well anchored at low levels of inflation can react to information quickly and in a sophisticated way as inflation rises and becomes more important for decisionmaking processes.

Ultimately, more empirical evidence is needed to understand how infla-tion and other expectations are formed. Experimental evidence, in par-ticular, can shed light on the questions raised by a large body of theoretical literature on models of expectation formation—such as adaptive, rational, and natural expectations (Fuster, Laibson, and Mendel 2010); and diagnos-tic expectations (Bordalo, Gennaioli, and Shleifer 2015). In particular, the evidence from Argentina suggests that perceived biases in the signals are capable of creating asymmetric responses in expectations. Future research should try to explain why this happens and to clarify the circumstances under which individuals tend to overreact or underreact to information.

Finally, in this paper, we focus on the effect of manipulating statistics on average inflation perceptions. In reality, the manipulation most likely affects other perceptions, such as uncertainty about inflation, which can have real effects on the economy. In other words, even if it was unsuccessful in reduc-ing the average perceived and expected inflation rates, the manipulation of statistics may have increased individual subjective uncertainty about infla-tion. Although we think it is unlikely, it is still possible that one of the gov-ernment’s goals behind the manipulation was precisely to obfuscate beliefs about inflation. Thus, more research is needed to understand the effects of potentially biased statistics on subjective uncertainty.

ACKNOWLEDGMENTS We thank the editors, Janice Eberly and James Stock, for their guidance in revising this paper. We also thank Robert Barro, Raj Chetty, Luciano Cohan, David Laibson, Roberto Rigobon, Guido Sandleris, Martin Tetaz, and Fernando Yu for their valuable comments, as well as those from seminar participants at Harvard University, the University of San Andrés, the MIT Sloan School of Management, and Torcuato Di Tella University. Julián


Amendolaggine, Martín Caruso, and Maria Fazzolari provided excellent research assistance. We also thank Carolina Yellati for her collaboration in conducting the survey experiment, and Guido Sandleris and Fernando Freijedo for the household inflation expectations survey data from the Finance Research Center (Centro de Investigación en Finanzas) at Torcuato Di Tella University. Fund-ing for this experiment was generously provided by the MIT Sloan School of Management and the Center for Distributive, Labor, and Social Studies (Centro de Estudios Distributivos, Laborales, y Sociales) at the National University of La Plata School of Economics. This project was reviewed and approved by the Committee on the Use of Humans as Experimental Subjects at MIT.


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Comments and Discussion

COMMENT BYSTEFAN NAGEL This paper by Alberto Cavallo, Guillermo Cruces, and Ricardo Perez-Truglia is an interesting one, and it studies a question that has not received much empirical attention. For the most part, we take it for granted that individual decisionmakers in the economy have access to high-quality data on important macroeconomic variables, such as inflation rates and GDP growth rates. Although macroeconomists have paid some attention to the noise in official statistics and the effect of data revisions, we know little about the effects of intentional manipulation of official macroeconomic statistics. This paper provides valuable new evidence on this question.

For thinking about the potential consequences of data manipulation, it is useful to first reflect on the benefits associated with a government’s provision of macroeconomic statistics. Because private sector agents could potentially learn from their own observations and through social learning channels, it is not entirely obvious how important government provision of macro-economic information really is. Though some exceptions have been noted in the literature, better public information is typically thought to be welfare-improving (Hellwig 2005). Furthermore, the existing evidence suggests that private sector agents rely to a substantial extent on official statistics when forming perceptions about current macroeconomic conditions and expecta-tions about conditions in the future. For instance, in an interesting study of a software bug that caused an error in the inflation statistics in Ecuador for several months, Paul Carrillo and Shahe Emran (2012) show that the error had a substantial effect on expectations.

The example from Ecuador is one of an accidental error, which is quite different from the intentional manipulation considered in this paper. In the case of Argentina considered here, the government’s intentions and its attempts at manipulation were probably quite clear—at least to parts of


the population. The paper provides quite convincing evidence that people in Argentina were not naively misled by the government’s manipulation. In terms of the posterior mean of the perceived inflation rate, individuals appeared to do quite a good job in debiasing the information provided in official inflation statistics. The effects on the posterior mean are the focus of the analysis in this paper. As I discuss in more detail below, the manipula-tion of statistics could potentially also have interesting and important effects on uncertainty about the inflation rate, not just on the posterior mean.

ASYMMETRIC REACTION TO INFLATION RATES In their online survey experi-ment, the authors present individuals with different official and unofficial inflation rates, and they elicit their inflation perceptions. Roughly speaking, subjects react to an official inflation rate of X percent in a similar way as to an inflation rate from unofficial sources of X + 10 percent. Thus, the differ-ence in their reaction is roughly in line with the magnitude that the actual bias in the inflation rate reported in the Consumer Price Index (CPI) seemed to have. On average, individuals’ processing of information seems to be quite well aligned with the authors’ simple Bayesian model. One interesting pattern—and one that is less straightforward to understand—is the asymme-try in individuals’ reaction to inflation rates at different levels. Varying the inflation rate that individuals are treated with from 10 to 20 percent (official or unofficial) produces a much smaller difference in subjects’ perception of the true inflation rate than moving from 20 to 30 percent. This effect does not quite fit with the authors’ normal prior–normal likelihood Bayesian model. To generate such an asymmetric reaction in the model, one probably needs to introduce some nonlinearity—for example, in the form of an upper bound of the bias. I suspect that if the bias was bounded above at zero, such an asymmetric reaction would arise within the model.

INTERPRETATION OF TREATMENT In the experiment, subjects are treated randomly with one of six inflation rates. Each of these represents a rate that was actually reported by a government agency or a private sector institution. The official inflation rates from the government agencies differ because they refer to different inflation indexes (CPI, GDP deflator, nomi-nal wage growth). During the period in question, the differences between these rates were substantial. Because the official rates used in the treatment are actually reported ones, just for different types of indexes, the authors consider their treatment to be nondeceptive. This may not be an entirely accurate characterization, because subjects are not being told to which offi-cial inflation index the rate with which they are treated refers. Because the CPI is the index with which subjects are presumably most familiar, most subjects probably think that the rates with which they are treated are CPI

COMMENTS and DISCUSSION 95

rates. In this sense, the experiment is effectively deceptive. Moreover, for the experiment to work as intended, this kind of deception is actually nec-essary. The authors want subjects to think that the official rates with which they are treated are CPI rates. The authors’ interpretation of the findings is based on the assumption that this deception was successful. However, because one cannot be sure that the deception worked perfectly, the reliance on deception complicates the interpretation of the results. When subjects are presented with, say, a high official inflation rate, do they infer, to some extent, that this could be nominal wage growth rather than CPI inflation? And as for the perceived inflation rate that they report to the experimenters, is this now their perceived CPI inflation rate or the perceived rate for some other basket or index?

PRICE CONTROLS The authors’ consumer-intercept survey shows little evi-dence that the government’s price controls that applied to certain types of products affected people’s perceived goods-specific inflation rates. Individ-uals’ recalled price changes are similar for both controlled and noncontrolled products. The authors’ conclusion is that the price controls did not affect people’s inflation perceptions. Though this is a plausible interpretation of the evidence, other interpretations are also possible. In particular, while indi-viduals may not be able to correctly recall product-specific price changes, it is still possible that price controls had an effect on their overall perceptions of inflation. Individuals’ recollections of the average price changes they expe-rienced could very well be affected by the price controls, even though they cannot quite recall correctly any product-specific price changes anymore.

The authors conclude from their evidence that “the government’s attempt to manipulate inflation expectations seems to have been ineffective and plausibly counterproductive.” This claim seems to be largely true, given the evidence in the paper, if one interprets it as meaning that the government’s manipulation had no effect on the mean of the perceived inflation distribution. It would be incorrect, however, to conclude from this that the government’s manipulation had no effect at all on the perceived inflation distribution. Fur-thermore, the fact that Argentina had a huge amount of outstanding inflation-linked bonds means that the manipulation may have resulted in a substantial wealth transfer away from the holders of these bonds.

UNCERTAINTY ABOUT INFLATION Although the government’s manipulation had little effect on the mean of consumers’ subjective posterior distribu-tion of inflation, the manipulation could have had a substantial effect on consumers’ uncertainty about inflation. The authors do not focus on uncer-tainty effects, and their experiments are not designed to measure effects on uncertainty, but the uncertainty channel could be an important one. As the


authors’ model shows, even with a fixed bias, the presence of the bias raises the posterior uncertainty about the inflation rate. The degree of uncertainty would be further magnified if one extended the model to allow for a ran-dom component in the bias. An elevated level of inflation uncertainty could lead to adverse economic consequences. For example, with more noise in the public inflation signal, firms might put more weight on idiosyncratic signals, leading to greater price dispersion and, as a consequence, misallo-cation. Price dispersion indeed seems to have grown following the manipu-lation; Andres Drenik and Diego Perez (2016) find a 13 percent increase in price dispersion in Argentina following the manipulation of the official inflation rate. It would be interesting to study in more detail to what extent a distortion of official inflation rates raises inflation uncertainty.

INFLATION-LINKED BONDS Even without any effect on consumers’ per-ceived inflation distribution, the policy could still be an effective one from the viewpoint of a (short-termist) government (and a nasty surprise for holders of inflation-linked bonds). At the start of the manipulation period, Argentina had about $50 billion worth of inflation-linked outstanding debt (Webber 2008). Inflation-linked bonds are supposed to protect investors’ real wealth against inflation, but they only do so if the inflation rate used in the calcula-tion of bond payments is not manipulated.

On each coupon date t, inflation-linked bonds pay a contractually fixed coupon rate times the ratio CPI(t)/CPI(0), where CPI(t) is the CPI level at the time of the coupon payment and CPI(0) is the CPI level at the time the bond was issued. Similarly, the principal paid back to bondholders at matu-rity T is a contractually fixed face value times CPI(T)/CPI(0). With $50 bil-lion worth of inflation-linked outstanding debt, downward manipulation of the inflation rate by 10 percent a year saves the government $500 million in coupon interest payments and $5 billion in accrued principal each year. In present value terms, if we take a 10-year, zero-coupon bond for a back-of-the-envelope calculation, a 10 percent downward manipulation of the CPI inflation rate over the life of the bond (that is unanticipated at the time of the bond issue) would amount to a 50 percent loss for bondholders and a gain of similar size for the government.

My figure 1 presents the “real” yield of Argentina’s inflation-linked bonds (constructed by Datastream as a weighted average across all outstanding maturities). In the case of Argentina, the usual calculation of a real yield no longer delivers the real yield once the government starts manipulating the inflation statistics. Instead, the “real” yield becomes

true real yield true inflation rate manipulated inflation rate.+ −


A downward bias in the official inflation rate thus raises the “real” yield that the usual calculation will deliver. In the extreme case where the gov-ernment manipulates the CPI inflation rate to zero, the “real” yield would equal the nominal yield on a nominal bond. In this case, inflation protec-tion has become completely ineffective and the bond trades like a nominal bond. As my figure 1 shows, the bond market is moving toward pricing inflation-linked bonds more like nominal bonds, as the “real” yield rises from about 5 percent in 2007 to close to 15 percent in 2008, consistent with the bias of about 10 percentage points in the official CPI inflation rate.1

Thus, from the viewpoint of the government, the manipulation of the CPI may have been highly effective in terms of its fiscal consequences, even if the policy did not succeed in affecting the mean of individuals’ perceived inflation distribution.

CONCLUSIONS Overall, this paper provides useful evidence on how indi-viduals dealt with manipulated official statistics in Argentina. Unofficial statistics are helpful as a substitute for information from official sources

1. The big jump in the “real” yield in late 2008 coincided with the announcement by Argentina’s government that it was nationalizing private pension plans. This rise in yields thus likely reflected different concerns, not the manipulation of the inflation rate.

Figure 1. The “Real” Yield of Argentina’s Inflation-Linked Bonds, 2004–15

Source: Datastream, code BEMA0Y.

Percent

Year

10

20

30

40

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015


and people are quite good in debiasing the numbers reported in the official statistics. Even so, it is important to keep in mind that the manipulation of the inflation rate in Argentina may have done harm in ways that are not studied in this paper. Manipulation could have substantial effects on infla-tion uncertainty with possibly detrimental welfare consequences. Further-more, manipulation may have resulted in a substantial wealth transfer away from holders of inflation-linked bonds.

REFERENCES FOR THE NAGEL COMMENT

Carrillo, Paul E., and M. Shahe Emran. 2012. “Public Information and Inflation Expectations: Microeconometric Evidence from a Natural Experiment.” Review of Economics and Statistics 94, no. 4: 860–77.

Drenik, Andres, and Diego J. Perez. 2016. “Price Setting under Uncertainty about Inflation.” Working paper. http://www.perezdiego.org/wp-content/uploads/ 2016/06/Drenik_Perez_2016.pdf

Hellwig, Christian. 2005. “Heterogeneous Information and the Welfare Effects of Public Information Disclosures.” Economics Online Paper no. 283. Los Angeles: University of California.

Webber, Jude. 2008. “Argentine Inflation Index under Fire.” Financial Times, June 11.

COMMENT BYRICARDO REIS This paper by Alberto Cavallo, Guillermo Cruces, and Ricardo Perez-Truglia provides a fascinating account of the extent to which the Argentine government manipulated inflation statistics between 2006 and 2015. The government enacted price controls, the common recipe to stop inflation that rarely works but is sure to distort relative prices and induce misallocation. More originally, the government changed the methodology used to construct price indexes, confirming an old fear among economists and statisticians that when given a range of possible estimates from alter-native methods, politicians behave as if picking from a menu rather than as Bayesians facing uncertainty. This culminated with the firing of high-ranking staff members of the Argentine government’s statistics bureau, the Instituto Nacional de Estadística y Censos (INDEC), going back to the old tradition of shooting the messenger when the message is not what politi-cians want.

The authors’ figure 1 describes most of the developments in this sad story of government manipulation of statistics; it is worth reading their paper just for this figure. The authors, however, are not political novelists but


top-notch economists, and true to their commitment to science, they resist the temptation to dwell on this story. Instead, they use it as a pretext to explain how people learn from statistics and form their inflation expectations. To stay focused on this goal, and to resist the siren call that comes from the authors’ figure 1, I take a step further and pose the question as if it were being applied to a less interesting country: the United States.

IMITATING THE SPIRIT OF THE AUTHORS’ EXPERIMENTS Imagine that I approach a crowd of economists and policymakers and ask:

What do you think was the annual U.S. inflation rate with respect to one year ago?

Note that I am asking for a fact about the past, not a forecast for the future. Yet surely I would get a distribution of answers. Even among a very-well-informed audience, some are better informed than others. Some are more confident or optimistic, and there is even some research suggesting that gender partly determines confidence, leading to disagreement. Some would interpret the question slightly differently from others, no matter how clear I try to be. From the raw distribution of answers, I would learn only one thing: People disagree and are not perfectly informed.

Imagine now that instead I randomize among my crowd of people, dividing them into six groups. I ask the first group:

According to official indicators published by the Bureau of Labor Statistics, the annual inflation rate with respect to one year ago was approximately 0.1 per-cent. What do you think was the annual U.S. inflation rate with respect to one year ago?

I would ask the second group exactly the same question, but replacing 0.1 percent with 1.4 percent. Finally, I would do the same with the third group, but now quoting a figure of 2.2 percent. What do you think the answers would be?

Perhaps my groups of survey respondents would just find the questions awkward, and repeat back to me the number that I had given them in the question. The distribution of answers across the three groups would then have three points, with exactly the same number of respondents in each.

Perhaps instead my respondents would have thought that I must be trick-ing them (why would I ask such a silly question anyway!?), and so would give me a different number from the one in the question. Still, my strong prior belief is that those in the first group would give lower answers than those in the second group, and lower even than those in the third group. As long as they put at least some weight on the possibility that the number that I was giving them had some credibility, it seems plausible that this would affect their estimate. And, by the way, my three numbers are not lies, but


come from the Bureau of Labor Statistics’ (BLS) Consumer Price Index (CPI) economic news release for January 2016: 0.1 percent, 1.4 percent, and 2.2 percent were the 12-month changes in the CPI for the Cleveland area, for all items in the nation, and for all items except food and energy.1

Alternatively, imagine that I ask the fourth group a different question:

According to other indicators published by the Bureau of Economic Analy-sis, the annual inflation rate with respect to one year ago was approximately -2.0 percent. What do you think was the annual U.S. inflation rate with respect to one year ago?

The fifth and sixth groups would get the same question, but with the num-bers 0.3 percent and 1.0 percent. Again, these are all true: The three num-bers refer to the change in the deflators for nondurable goods, personal consumption expenditures, and gross domestic product.

My guess is that again the fourth group would expect lower inflation than the fifth, and even lower than the sixth. I would also venture that there would be differences in the distribution between these three groups and the previous three. My informed respondents would note that I refer in the question to these indicators as other rather than official, perhaps increas-ing their suspicion toward me. Moreover, they would know that the more commonly used measure of inflation is the CPI computed by the BLS, not the deflators computed by the Bureau of Economic Analysis, so they might regard this information as not quite as reliable as the previous one.

In essence, this is what the authors do in their surveys of Argentines. Their respondents are not as trained in economics and statistics as my hypo-thetical ones, even if they are more educated than the typical Argentine, and they are used to living in a country that often faces high and volatile inflation, making them more attentive to this economic indicator. To be clear, with my thought experiment, I do not want to undermine the authors’ remarkable work designing and implementing these surveys, nor to under-value how important it is to go from thought experiments to actually collect-ing data that may well end up challenging one’s priors. My goal is instead to focus on what information was being given to the respondents and what was being asked of them, so I can proceed to discuss what we may or may not learn from it.

WHAT CAN WE LEARN FROM THE RESULTS? The first result that the authors obtain is that providing information has an effect on the answers that

1. BLS, “Consumer Price Index: January 2016,” news release, February 19, 2016 (http://www.bls.gov/news.release/archives/cpi_02192016.pdf).


people give. My six groups described above would not have given the same answer if they were like the Argentines in the authors’ sample. The authors read this as a triumph for the Bayesian proposition that people do not ignore valuable pieces of information, but use them to update their priors toward new posteriors.

I agree. But this is also a fairly low bar. Only if the information were absolutely and completely useless would a Bayesian ignore it. All six num-bers that I provided in my hypothetical survey, and likewise the authors’ six numbers in the actual survey, were not just true but also definitely informa-tive about what inflation must be. Even in the case of the biased govern-ment statistics, the respondents to the authors’ survey certainly had some information about true inflation, even if it was muddled by the govern-ment’s manipulations. Moreover, one would expect that even if the infor-mation provided was indeed useless, the people receiving it in the way described in the interview might well presume that it was somewhat useful.

Moreover, even a non-Bayesian would be expected to react to this infor-mation. Endless psychological studies have shown that cues affect responses. Providing a number, even if it is arbitrary and useless, anchors future responses to questions that ask for numbers (Tversky and Kahneman 1974). Moreover, the very-well-known Hawthorne effect states that subjects of a study have their behavior affected by being aware that they are being observed. In the case of this survey, this would likely lead even a non-Bayesian to have the number that they were given in the question affect his or her answer, even if this number had no effect on their actual expectations of inflation and on their subsequent economic choices. Having an inter-viewer tell you that inflation is 0.1 percent makes it hard for you to reply that it is actually 10 percent, even if this is what you really think.

The second result is that the distribution of answers across the groups that were given the official statistics is different from the distribution of answers in the group given the alternative indicators. In terms of my exper-iment above, the distribution across the first three groups would be differ-ent from the distribution across the last three groups.

More precisely, the authors show that people’s answers are consis-tent with the hypothesis that when receiving information from the official Argentine indicators, they subtract a constant 10 percent perceived upward bias. Thus, the distribution of answers for a group that is told that an offi-cial statistic is 20 percent is similar to the distribution for a group that is told that an alternative indicator is 10 percent. In symbols, if the distribu-tion of answers after an unofficial statistic is revealed appears to be drawn from some distribution with mean x and variance y, then the distribution


of answers after an official statistic is revealed seems to be drawn from a similar distribution, which is different only in having a mean x - b, where b is the bias.

These results are again persuasive, and the differences across groups can be easily inferred visually. At the same time, failing to reject the null hypothesis that people behave as if there was a constant mean bias is not the same as accepting this hypothesis about people’s behavior. Consider two alternatives. First, perhaps the bias is multiplicative, so that, instead, the distribution following the official numbers has a mean of bx. Would the data reject this alternative? Second, perhaps there is no bias but rather a perception of different precision or informativeness such that the distribu-tion after the official number has the same mean but a variance of by. The authors’ data would have trouble distinguishing this alternative.

Moreover, bias is not the same as cheating. We know that the CPI mea-sures produced by the BLS suffer from substitution bias. Since the 1996 Boskin Commission Report, a common rule of thumb in the United States has been to subtract about 1.3 percent from the CPI statistic to get closer to the true cost of living.2 But few people see in this any form of cheating by the BLS.

The third result of this paper is that there is an asymmetry in people’s responses. Because they distrust the official sources as understating infla-tion, people respond more to official statistics that report higher inflation than to official statistics reporting lower inflation. The argument goes that for the government to be reporting high inflation, then actual inflation must be really high, to the point where it cannot be hidden anymore.

Interestingly, however, the asymmetry is also there in the distribution of responses that people gave after being told an unofficial inflation statistic. This suggests that the source of the asymmetry is not driven by the data they are provided, but rather by the person’s responses to any information. On one hand, this may be because people in Argentina have learned to dis-trust any inflation number, regardless of its source. On the other hand, it may be the result of forming forecasts while having an asymmetric loss function in their mind. Insofar as higher inflation causes real income losses, and there is diminishing marginal utility from this income, this could justify such an asymmetry.

2. Social Security Administration, “The Boskin Commission Report: Toward a More Accurate Measure of the Cost of Living—Final Report to the Senate Finance Committee from the Advisory Commission to Study the Consumer Price Index, December 4, 1996” (https://www.ssa.gov/history/reports/boskinrpt.html).


The authors’ three results are solid and hard to dispute. As often hap-pens, however, the results are open to more than one interpretation.

WHAT CAN WE CONCLUDE ABOUT LEARNING? A separate question is whether the authors’ methods, survey answers, and statistical analysis allow us to reach broader conclusions about learning and data. The authors are careful not to claim these conclusions; but it is the role of the discussant to specu-late about whether they do.

First, can we conclude that their survey methodology is able to isolate the effects of information on expectations? Some notation is helpful to understand the authors’ method. Let person i’s prior answer on what was inflation in the past 12 months be aprior (i). After receiving the piece of data from the interviewer, the person will have a posterior apost (i). People are sorted into two groups: those treated with the official inflation reports, in group T; and those in the control group who do not receive this informa-tion, in group C. The goal is to estimate information’s effect on the revi-sion of people’s answers as a result of the treatment, which can be done by comparing the two sample means:

.∑ ∑[ ] [ ]( ) ( ) ( ) ( )− − −∈ ∈

a i a i a i a ipost prior

i T

post prior

i C

However, the authors did not elicit the priors, so they do not observe aprior (i). As a result, their statistics are instead based on

.∑ ∑( ) ( )−∈ ∈

a i a ipost

i T

post

i C

Clearly, this is a valid measure only as long as

.∑ ∑( ) ( )=∈ ∈

a i a iprior

i T

prior

i C

The reason why we expect this to be the case is through the random-ization of people into treatment and control groups. If this randomization ensured that being part of each of the two groups is not correlated with any important source of differences across people’s inflation expectations, then this condition would hold. The authors’ sample plausibly satisfies this condition. The only source of concern is that their sample has a larger share of women than the population, 57 percent versus 53 percent, and there is a weak suggestion in the literature that women’s inflation expectations are systematically different from men’s (Bryan and Venkatu 2011).


Second, can we use their method to conclude that there is a constant inflation bias in the official data that people rationally take into account when using data from official sources to form their inflation expectations? This is a significantly harder question. The authors persuasively show that one cannot reject the null hypothesis that there is a constant 10 percent inflation bias that people take into account. But the flexibility of Bayes’s rule does not allow us to confidently pin down whether the bias exists, whether it is constant, or whether it is 10 percent. With only their data, but with freedom to choose people’s loss function for making forecasts and freedom to choose the two distributions from which the signals on inflation are drawn, the official and the alternative one, then we could get almost any estimate of the bias. Bayes’s rule is very flexible and can accommodate many different patterns of responses.

Third, can we conclude that agents are sophisticated Bayesians, ratio-nally discounting biased data? Again, the authors convincingly show that this null hypothesis is hard to reject. In fact, their results are even stron-ger. They support the modern theories of inattention, according to which the disagreement that we observe is due to people not having the same information, but once people get to pay attention—for instance, because an interviewer gives them information—they rationally update their beliefs (Reis 2006).

At the same time, the data have two features that are harder to reconcile with this optimal inattentiveness. First, why would Argentines—who by many accounts are quite informed about inflation, having lived through great price volatility many times in the recent past—have such loose priors? The authors’ data show that giving one single number in an inter-view has a large effect on people’s perceptions of inflation, which must imply that they were quite uncertain about it in the first place. Second, why do perceptions of past inflation line up so closely with expectations of future inflation (as seen in the authors’ figure 5)? The serial correlation of inflation is well below 1 in the Argentine data, so this extent of persis-tence in perceptions and forecasts will likely lead to serially correlated forecasting errors.

ARE ARGENTINES UNSOPHISTICATED AFTER ALL? Having made a case for Argentines being quite sophisticated in using official manipulated data and forming inflation expectations, the authors move in a different direc-tion in section III. Here, they show the result from asking people outside a supermarket about the historical price changes of the goods they have just bought. Conceptually, this is a very different question from the one


considered in the rest of the paper. Here, it is not inflation—the general increase in prices for a wide basket of goods—that people are being asked about, but rather the prices of the individual goods they bought minutes ago and how they compare with what people think these prices were 12 months ago.

Impressively, the authors show that even though the Argentine govern-ment had imposed strict price controls on some goods during this period, people’s perceptions of how these goods’ prices changed, relative to those goods whose prices were free from government meddling, were essentially the same. This form of government manipulation—here, not of statistics but of goods’ prices themselves—seems to again have had little effect on the Argentine public.

However, another conclusion is striking: Remembered price changes are extraordinarily higher than actual price changes, as shown in the authors’ figure 7. Although fewer than 5 percent of prices changed by more than 60 percent, people answer that more than 40 percent of prices changed by this amount or more. By this account, Argentines’ answers are so far off from the facts that they seem quite remarkably unsophisticated.

CONCLUSION This paper has two goals, and thus its results have two possible takeaways. The first is that in Argentina, people do not let the manipulation of official statistics and prices fool them. Even as the gov-ernment seemed to bias official statistics down or to control the price changes of individual goods, the public’s perceptions of actual infla-tion and future inflation remained high. Government data were debiased rather than taken at face value, and branding a piece of data as “official” led the public to treat it differently right away. Reality seemed to prevail over propaganda.

The second takeaway pertains to people’s sophistication in forming per-ceptions about inflation. Here the bag is more mixed. In some respects, Argentines seem quite sophisticated; but in others, they are remarkably biased. The authors’ data and statistics provide very valuable information with which to judge models of the formation of expectations, but they are not quite decisive toward any one particular theory.

Perhaps this paper’s overall lesson, especially for policymakers, is that in spite of all the studies and research showing that people are far from rational in forecasting inflation, it does not follow that policymakers can therefore easily manipulate people’s views. People may not be all that rational in dealing with economic data and forecasts, but they are experi-enced enough not to be duped by their governments.


REFERENCES FOR THE REIS COMMENT

Bryan, Michael F., and Guhan Venkatu. 2001. “The Curiously Different Inflation Perspectives of Men and Women.” Economic Commentary. Federal Reserve Bank of Cleveland.

Reis, Ricardo. 2006. “Inattentive Consumers.” Journal of Monetary Economics 53, no. 8: 1761–800.

Tversky, Amos, and Daniel Kahneman. 1974. “Judgment under Uncertainty: Heuristics and Biases.” Science 185, no. 4157: 1124–31.

GENERAL DISCUSSION Justin Wolfers opened the discussion with some “clownish” facts about unemployment and inflation beliefs in the United States. According to a recent survey, 34 percent of Americans believe that unemployment is higher today than when President Barack Obama took office, with 53 percent of Republicans believing this.1 A dif-ferent statistic, something a little closer to the sense of the paper, is that there is a faction in the United States that believes that official CPI sta-tistics are being terribly manipulated. Subscribers to the electronic news-letter service Shadow Government Statistics (www.shadowstats.com) can pay $175 per year to learn what the “real” inflation rate is. “That $175 a year,” he joked, “what they’ll do is they’ll take the CPI and add 8 points to it for you.” Ironically, he noted, the price of the subscription has not changed in eight years, implying “a substantial real price cut in the price of ShadowStats.”

Both of these statistics, Wolfers noted, move the focus away from the mean of expectations to the distribution, which produces very different views about the world. What the paper shows is that the mean of expecta-tions moves in a sensible way. However, looking at the micro data on any expectations, “Most people have completely stupid expectations.” The first moment is not going to be enough; one needs to know the full distribution. “It might be that the full distribution story is people move from completely clueless to completely clueless,” he concluded, which is a different story than people being quite sophisticated in debiasing.

Marshall Reinsdorf described Argentina as a very decentralized country, and remarked that one of the many fascinating things for him about Argen-tina during the 2006–15 period studied in the paper were the differences between the various provincial inflation rates. Looking at a random sample

1. In fact, the official U.S. unemployment rate in January 2009 was 7.8 percent; in January 2016, it was 4.9 percent.


of five Argentine provinces, he noted that one reported an inflation rate of 40 percent, two reported inflation rates of 30 percent, and two reported inflation rates of 10 percent. He suggested that an interesting experi-ment might be to compare reactions to inflation statistics across prov-inces, and wondered if this sort of experiment might be possible.

Wojciech Kopczuk had two questions. First, he wondered to what extent black market prices and other ways of pricing were prevalent in Argen-tina. Specifically, he noted that the most important black market price that is easy to observe is the exchange rate. The exchange rate is informative about other prices, so it is interesting to explore to what extent it factors into perception of the bias and how people are reacting to information. Sec-ond, he wondered to what extent people actually understood what inflation is. Fundamentally, the price level is measured relative to a basket of goods, but most people probably have different ideas about what sorts of items are included, especially in the presence of price controls. For instance, if some prices are fixed, one might not want to include them in the average.

Carol Graham pointed out that she grew up in Latin America, where hyperinflation was rampant. She noted that even very poor people seemed to be sophisticated about things like inflation and consumer baskets. For instance, workers will get their wages in whatever the home currency is and cash them in for dollars at night; they are very well aware of what the exchange rate is, in a way that most people in the United States just are not because they are not living with hyperinflation. Any kind of hyperinflation becomes a way of living, of trying to survive. She warned not to underesti-mate the sophistication of consumers in this story.

Joe Beaulieu made one minor point. As had been suggested, it was a very interesting idea to look at the effect of the dispersion of prices once the Argentine government had introduced its new policies toward index-ation. He cautioned that at the same time, there appeared to be a sharp increase in inflation, and that there is a fairly robust fact in the literature that the two are related in all sorts of ways, both in terms of inflation rates and the actual dispersion of prices.

Alberto Cavallo noted that most people in Argentina do in fact know what inflation is. On the question of price controls, Cavallo stated that the authors looked at not only how price controls affected how Argentines remembered prices but also whether they affected expectations. They found that price controls did not significantly affect expectations. Surpris-ingly, they also found that price controls did not lead to shortages, the rea-son being that the government very quickly moved from undertaking a massive price control program to setting highly targeted price controls.


In his presentation, discussant Stefan Nagel had noted that there appears to be a puzzling asymmetry, or downward stickiness, in people’s percep-tions of inflation. For example, at lower levels of reported inflation—say, 10 or 20 percent—there were relatively small differences in perceived inflation. However, at higher levels of reported inflation—say, 20 or 30 percent—there seemed to be a much bigger difference in perceived inflation. Cavallo argued that the asymmetry appears to only be present in government statis-tics, not in the prices of goods.

Nagel had one additional comment for the authors. He wondered, when it came to paying off the holders of inflation-linked bonds, whether the Argentine government unrigged the official numbers. Cavallo responded in the negative, and noted that the only time the government unrigged them was in January 2014, when it realized that if it ever wanted to bor-row again, it would need to clean up its act. The government launched a new CPI, which did not recognize any prior data; as a result, bondholders were swindled.

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Learning from Potentially Biased Statistics · 2016-08-05 · In this paper, we study how ... als to spend time gathering and processing information about the inflation ... that there